Probabilistic Analysis using Theorem Proving

Traditionally, computer simulation techniques are used to perform probabilistic analysis. However, they provide less accurate results and cannot handle large-scale problems due to their enormous CPU time requirements. Recently, a significant amount of formalization has been done in higher-order logic that allows us to conduct precise probabilistic analysis using theorem proving and thus overcome the limitations of the simulation based probabilistic analysis approach. Some major contributions include the formalization of both discrete and continuous random variables and the verification of corresponding probabilistic and statistical properties. This book presents a concise description of the infrastructures behind these capabilities and their utilization to conduct the probabilistic analysis of real-world systems. The case studies of the round-off error of a digital processor, the Coupon Collectors problem and the Stop-and-Wait protocol are used to illustrate the proposed analysis approach. Designed as an independent research tool, the book presents a well-thought-out treatment of a rapidly emerging multidisciplinary field across Mathematics, Computer Science and Engineering.